In the figure shown, \overline{U S} and \overline{U T} are line segments each of length 2 , and m \angle T U S=60^{\circ}. Arcs T R and S R are each one-sixth of a circle with radius 2 . What is the area of the region shown?
Answer Choices
A. 3 \sqrt{3}-\pi
B. 4 \sqrt{3}-\dfrac{4 \pi}{3}
C. 2 \sqrt{3}
D. 4 \sqrt{3}-\dfrac{2 \pi}{3}
E. 4+\dfrac{4 \pi}{3}